o19 Modelling of Combined reinforcement of Ceramic Composites by Whisker and Transformation Toughening G. M. Song, Y Zhou, Y Sun &T C. Lei School of Materials Science and Engineering, PO Box 433, Harbin Institute of Technology, Harbin 150001 People's Republic of China ( Received 10 April 1997; accepted 30 May 1997) Abstract: An appropriate model of combine toughening in ceramic composites toughened with whiskers and transformation particles is presented to identify the effects of whisker toughening and transformation toughening. whisker tougher ing includes whisker bridging and crack deflection. For transformation toughen- ng, the shear effect is considered by using a shear factor, based on the dilatation contribution. Calculated results show that there are interactions among whisker bridging, crack deflection and transformation toughening. Crack brid- ging and crack deflection give rise to the contribution of transformation tough- ening, but transformation toughening produces a reduce to the contributions of whisker bridging and crack deflection. Predictions of the toughness of ZrO2(2mol%Y203)/Al2O3 based on the present model are showed to be in good agreement with the experimental results. c 1998 Elsevier Science Limited and Techna S.r.I 1 INTRODUCTION Several theoretical analyses of fibre bridging in fibre-reinforced ceramics has been proposed.9,0A Whisker is found to be effective in strengthening continuum model is introduced by Budiansky et and toughening ceramic materials, - and the al. for an elastic solid which contains particles toughening is realised by main three toughening that undergo an irreversible stress-induce dilation mechanisms, whisker bridging, whisker pullout and transformation. A model which includes both crack deflection. On the other hand toughness has shear and dilation effects of transformation tough been improved remarkably by ZrO2 1-m transfor- ening, has also been established, 2 which is perhaps mation in many ceramics --b Toughness values can more realistic than the early model which considers further be increased when both whiskers and parti- dilatation only. Amazigo et al. 3 also presented a cles are incorporated into ceramic matrix. In some analysis model of synergistic toughening including cases, synergistic toughening has been observed and crack bridging by ductile particles and dilation lized.7.In the combine toughened ceramics with transformation of ZrO2 particles both Sic whiskers and Zro transformation parti Whisker is a kind of short fibre and its orienta- cles, there are various toughening mechanisms that tion in ceramic matrix is usually random, which operate simultaneously, including whisker bridging, different to unidirectional aligned long fibre. Crack crack deflection, whisker pullout, microcracking deflecting along whisker/matrix interfaces is very and transformation, etc. du uring crack propagating. frequently observed. Addition of ZrOz transfo It is very difficult to identify experimentally th mation particles in whisker-toughened ceramics relative contribution and the role of each toughen- makes toughening analysis more complicated To ing mechanism. So theoretical modelling of com- date, there is not a suitable model to discuss bine toughening in ceramics toughened by multiple this problem of combine toughening with both toughening methods is a long standing subject whiskers and Zro2 transformation particles
Modelling of Combined Reinforcement of Ceramic Composites by Whisker and Transformation Toughening G. M. Song, Y. Zhou, Y. Sun & T. C. Lei School of Materials Science and Engineering, PO Box 433, Harbin Institute of Technology, Harbin 150001, People's Republic of China (Received 10 April 1997; accepted 30 May 1997) Abstract: An appropriate model of combine toughening in ceramic composites toughened with whiskers and transformation particles is presented to identify the eects of whisker toughening and transformation toughening. Whisker toughening includes whisker bridging and crack de¯ection. For transformation toughening, the shear eect is considered by using a shear factor, f, based on the dilatation contribution. Calculated results show that there are interactions among whisker bridging, crack de¯ection and transformation toughening. Crack bridging and crack de¯ection give rise to the contribution of transformation toughening, but transformation toughening produces a reduce to the contributions of whisker bridging and crack de¯ection. Predictions of the toughness of SiCw/ ZrO2(2mol%Y2O3)/Al2O3 based on the present model are showed to be in good agreement with the experimental results. # 1998 Elsevier Science Limited and Techna S.r.l. 1 INTRODUCTION Whisker is found to be eective in strengthening and toughening ceramic materials,1±3 and the toughening is realised by main three toughening mechanisms, whisker bridging, whisker pullout and crack de¯ection.3 On the other hand, toughness has been improved remarkably by ZrO2 t±m transformation in many ceramics.4±6 Toughness values can further be increased when both whiskers and particles are incorporated into ceramic matrix. In some cases, synergistic toughening has been observed and utilized.7,8 In the combine toughened ceramics with both SiC whiskers and ZrO2 transformation particles, there are various toughening mechanisms that operate simultaneously, including whisker bridging, crack de¯ection, whisker pullout, microcracking and transformation, etc., during crack propagating. It is very dicult to identify experimentally the relative contribution and the role of each toughening mechanism. So theoretical modelling of combine toughening in ceramics toughened by multiple toughening methods is a long standing subject. Several theoretical analyses of ®bre bridging in ®bre-reinforced ceramics has been proposed.9,10 A continuum model is introduced by Budiansky et al.11 for an elastic solid which contains particles that undergo an irreversible stress-induce dilation transformation. A model which includes both shear and dilation eects of transformation toughening, has also been established,12 which is perhaps more realistic than the early model which considers dilatation only. Amazigo et al.13 also presented a analysis model of synergistic toughening including crack bridging by ductile particles and dilation transformation of ZrO2 particles. Whisker is a kind of short ®bre and its orientation in ceramic matrix is usually random, which is dierent to unidirectional aligned long ®bre. Crack de¯ecting along whisker/matrix interfaces is very frequently observed. Addition of ZrO2 transformation particles in whisker-toughened ceramics makes toughening analysis more complicated. To date, there is not a suitable model to discuss this problem of combine toughening with both whiskers and ZrO2 transformation particles. Ceramics International 24 (1998) 521±525 # 1998 Elsevier Science Limited and Techna S.r.l. Printed in Great Britain. All rights reserved PII: S0272-8842(97)00051-5 0272-8842/98 $19.00+.00 521
522 G. M. Song et al Our previous experimental investigations on SIC Due to the geometric relation hisker-ZrO, toughened Al,O, ceramics",8 show that whisker bridging, crack deflection and trans- p=bcos2φ ls cos formation are the main toughening mechanisms in these composites. In this paper, we try to provide a where oy is the crack cohesive stress from bridging simple model of combine toughening, including whisker, uy is the crack face opening distance. then whisker bridging, crack deflection and transforma tion, to analyse quantitatively combine toughening a,=2 cos/2p(Ewt(1 +n)/r] yuy of whiskers and transformation particles, and the alidity of this model is also identified by using For a single notch specimen(Fig. 2), the whisker ome experimental resul bridging contribution is given by △Kb= 2VrO,(u,(x)) 2 THEORETICAL MODEl √ma H(a/w, x/a)dx (5) where H(a/W, x/a)is a weight function. 5 2. 1 Whisker toughening In most whisker-reinforced ceramics. the crack deflection is usually observed, but the deflected When a crack meets with a incline whisker, the distance along with whisker/matrix is often much whisker /matrix interface usually debonds and the less than the half length of whisker. The crack sur whisker slips over a certain distance, Ls(Fig. 1). face area is enlarged by crack deflection, so the suming the incline whisker is not bending during toughening contribution associated with the crack le crack face opening process, the relation surface area can be calculated. Assuming the max between the axial stress and the axial extension of imum deflection length, Ld, equals the slipping the whisker into the crack face can be obtained distance, Ls, the resultant toughness from the according to the shear-lag model. 9 additional surface area can be given by assuming that fracture surface morphology comprises cones o=2En(1+n)/rm]2√ (1)(height, o to Ld) where n= EwVw/(EmVm), Ew and Iw are the Youngs modulus and the radius of the whisker 5)+(Lsin(6 respectively, and t is the whisker /matrix interfacial shear stress14 where Ya, Ym are the strain energy release rates of T=HAaAT/(1+Vm/2Em+(1-2vw)/Ew](2) deflected and undeflected crack, where 8 is the centre to centre nearest neighbour spacing between where u is the interfacial friction coefficient, Aa is whiskers. 6 Equation(6) implies the influence of the coefficient differential of thermal expansion, interface bonding strength effect on crack deflec- AT is the temperature differential between the tion through Ls. Then the crack deflection contri- temperature below which stress relaxation cannot bution is simply given by take place and the temperature under considera- tion and v is poissons ratio 2.1.1 Transformation toughening When a macroscopic crack propagates in a ceramic matrix containing Zro, transformation particles P a cTOD Fig. 1. An incline whisker bridging a crack Fig. 2. A single-edged notch 3-point bending specimen
Our previous experimental investigations on SiC whisker±ZrO2 toughened Al2O3 ceramics7,8 show that whisker bridging, crack de¯ection and transformation are the main toughening mechanisms in these composites. In this paper, we try to provide a simple model of combine toughening, including whisker bridging, crack de¯ection and transformation, to analyse quantitatively combine toughening of whiskers and transformation particles, and the validity of this model is also identi®ed by using some experimental results. 2 THEORETICAL MODEL 2.1 Whisker toughening When a crack meets with a incline whisker, the whisker/matrix interface usually debonds and the whisker slips over a certain distance, Ls (Fig. 1). Assuming the incline whisker is not bending during the crack face opening process, the relation between the axial stress and the axial extension of the whisker into the crack face can be obtained according to the shear-lag model.9 2 Ew 1 =rw 1=2 u p 1 where EwVw= EmVm , Ew and rw are the Young's modulus and the radius of the whisker, respectively, and is the whisker/matrix interfacial shear stress14 T= 1 m =2Em 1 ÿ 2w =Ew 2 where is the interfacial friction coecient, is the coecient dierential of thermal expansion, T is the temperature dierential between the temperature below which stress relaxation cannot take place and the temperature under consideration, and is Poisson's ratio. Due to the geometric relation y cos2 uy u cos 3 where y is the crack cohesive stress from bridging whisker, uy is the crack face opening distance. then y 2 cos3=2 Ew 1 =rw 1=2 uy p 4 For a single notch specimen (Fig. 2), the whisker bridging contribution is given by Kb a a0 2Vwy uy x ÿ a p H a =W; x=a dx 5 where H a =W; x=a is a weight function.15 In most whisker-reinforced ceramics, the crack de¯ection is usually observed, but the de¯ected distance along with whisker/matrix is often much less than the half length of whisker. The crack surface area is enlarged by crack de¯ection, so the toughening contribution associated with the crack surface area can be calculated. Assuming the maximum de¯ection length, Ld, equals the slipping distance, Ls, the resultant toughness from the additional surface area can be given by assuming that fracture surface morphology comprises cones (height, 0 to Ld) yd=ym 2 2 =2 0 2 2 Ls sin 2 s d 6 where Yd, Ym are the strain energy release rates of de¯ected and unde¯ected crack, where is the centre to centre nearest neighbour spacing between whiskers.16 Equation (6) implies the in¯uence of interface bonding strength eect on crack de¯ection through Ls. Then the crack de¯ection contribution is simply given by Kd yd=ym p ÿ 1 Km 7 2.1.1 Transformation toughening When a macroscopic crack propagates in a ceramic matrix containing ZrO2 transformation particles. Fig. 1. An incline whisker bridging a crack. Fig. 2. A single-edged notch 3-point bending specimen. 522 G. M. Song et al
Modelling of combined reinforcement of ceramic composites 523 The ZrO2 in the vicinity of the crack tip will take place t-m transformation and a transformation zone is formed(Fig. 3). It is assumed that the transformation zone is comprised of a continuum of dilation particles near crack tip. The hydrostatic stress,Em(=3Ei, i= l, 2, 3), applied on each dilation particle is given b 2m =20+)Pcos(0/2) where Kp is the elastic intensity factor determined for the actual geometry of a cracked specimen at a Fig. 3. Schematic of combine toughening of whisker and given load P, r and 0 are the position co-ordinates of an expansion center relative to the crack tip, v is Poissons ratio If Em reaches a critical value, ac, t-m transfor- crack. We still assume that the whole crack is a mation will occur including a dilation of about 4% mode I crack, although the crack is deflected in the and a shear distortion of about 7%.6 A uniform vicinity of the crack tip. As a is the angle between dilation transformation of a ZrOz particle will the crack faces, the crack opening displacement, produce a reduction in near crack-tip intensity 2u,(x), at point x is relative to the applied intensity, and the stress intensity factor induced is 2uy=a(a-x)(ao≤x≤a) (11) Ak=(Gcos(3/2)1/(2 m) "x p2 dA (9) then the crack tip opening displacement CTOD is where G is the shear modulus and da is the volume dilation strain of each Zro, particle When u(x)>uy(2uyc is the critical opening dis- A shear strain, &r, and dilation, e, take place placement of the crack face), the whisker at point x multaneously during a Zro 2 particle transform- will break and the crack closure stress o, (x)Vw=0o ing, and the toughening contribution of the shear The stress intensity factor K, due to the external strain is of the same order of magnitude as that of oad p is the volume dilation. 2 To simplify the calculation of the contribution from transformation toughen 2Bn VaF(a/w) ing, we presume a shear strain factor, f, which reflects the effect of shear strain. So the transfor. mation effect from both shear strain and dilation where F(a/w is a weight function. 5 strain can be obtained by As a crack propagates, the fracture resistance K, △K=V=mG(f+ cos(30/2)/(2x)r32 Kr=Km+△Kx+△Kb+△Kd rare (10) where Km is the fracture toughness of the matrix, and△Ky,△ Kh and△ Kd are the contributions of transformation, whisker bridging and crack deflec where A denotes the region of the transformation tion, respectively. Equation (14)includes three zone, (1+f is assumed to represent shear strain toughening mechanisms, transformation, whisker and dilation and V_m is the volume fraction of the bridging and crack deflection ZrO which takes place t-m transformed in the total zro 3 EXPERIMENTAL PROCEDURE 2.1.2 Fracture resistance equation For the notch specimen, the initial notch length, ao, Al2O3 powder with a average size of about 0.1 um is much longer than the crack growing length, is used as the basic material ZrO2 powder stabilised a(= a-ao), until the instable propagation of the by 2mol%Y203 and Sic whisker was prepared as
The ZrO2 in the vicinity of the crack tip will take place t±m transformation and a transformation zone is formed (Fig. 3). It is assumed that the transformation zone is comprised of a continuum of dilation particles near crack tip. The hydrostatic stress, m 1 3 ii; i 1; 2; 3 ÿ ), applied on each dilation particle is given by m 2 1 3 Kp 2r p cos =2 8 where Kp is the elastic intensity factor determined for the actual geometry of a cracked specimen at a given load P, r and are the position co-ordinates of an expansion center relative to the crack tip, is Poisson's ratio. If m reaches a critical value, c, t±m transformation will occur including a dilation of about 4% and a shear distortion of about 7%.6 A uniform dilation transformation of a ZrO2 particle will produce a reduction in near crack-tip intensity relative to the applied intensity, and the stress intensity factor induced is k G cos 3=2 = 2 1=2 r 3=2 h idA 9 where G is the shear modulus and dA is the volume dilation strain of each ZrO2 particle. A shear strain, "r , and dilation, "T, take place simultaneously during a ZrO2 particle transforming, and the toughening contribution of the shear strain is of the same order of magnitude as that of the volume dilation.12 To simplify the calculation of the contribution from transformation toughening, we presume a shear strain factor, f, which re¯ects the eect of shear strain. So the transformation eect from both shear strain and dilation strain can be obtained by Ks VtÿmG f 1 "T cos 3=2 = 2 1=2 r 3=2 " # rdrd 10 where A denotes the region of the transformation zone, (1+f) is assumed to represent shear strain and dilation, and Vtÿm is the volume fraction of the ZrO2 which takes place t±m transformed in the total ZrO2. 2.1.2 Fracture resistance equation For the notch specimen, the initial notch length, a0, is much longer than the crack growing length, a a ÿ a0), until the instable propagation of the crack. We still assume that the whole crack is a mode I crack, although the crack is de¯ected in the vicinity of the crack tip. As is the angle between the crack faces, the crack opening displacement, 2uy x , at point x is 2uy a ÿ x a0 x a 11 then the crack tip opening displacement CTOD is CTOD a ÿ a0 12 When u x uyc (2uyc is the critical opening displacement of the crack face), the whisker at point x will break and the crack closure stress y x Vw 0o. The stress intensity factor Kp due to the external load P is Kp 3PL 2BW2 a p F a =W 13 where F a =W is a weight function.15 As a crack propagates, the fracture resistance Kr is Kr Km Ks Kb Kd 14 where Km is the fracture toughness of the matrix, and Ks, Kb and Kd are the contributions of transformation, whisker bridging and crack de¯ection, respectively. Equation (14) includes three toughening mechanisms, transformation, whisker bridging and crack de¯ection. 3 EXPERIMENTAL PROCEDURE Al2O3 powder with a average size of about 0.1m is used as the basic material. ZrO2 powder stabilised by 2mol%Y2O3 and SiC whisker was prepared as Fig. 3. Schematic of combine toughening of whisker and transformation. Modelling of combined reinforcement of ceramic composites 523
524 G. M. Song et al reinforcements. According to the proportion of rapid rise in fracture resistance, Kr. For further AlO3+(10, 20, 30 vol%)ZrO2+(10, 20, 30 vol%) crack extension, a higher value of the applied Kp is SiCw, these powders and whiskers are mixed by required. With the further crack propagation, due ball milling for 24 h in an hydrous alcohol to some whiskers which bridge the crack failing, a mixtures are dried and green-compacted at transformation wake zone is formed, the increase 250 MPa and then hot pressed at 1650%C, 25 MPa in AKs and AKb no longer rise remarkably, thereby for 45 min. The temperature lies for hot pressing in the slope of R-curves gradually drops, and these the single tetragonal phase region of ZrO2-Y2O3 curves will also tend to become parallel lines diagram. The fracture toughness is measured with The effective fracture toughnesses calculated are an Instron-1 186 testing machine using the single- shown in Tables I and 2. For the same Zro2 con- edge notch3- point bend specimen,30×4×2, with a tent,△Ks,△ Kh and△ Kd increase with increasing notch depth, 2 mm. The volume percentage of I- whisker content, as shown in Table l, it implies ZrO2 in total ZrO2 is measured with X-ray diffrac- that an increment in whisker content will give rise tion(XRD)on the as-polished and the fracture to each contribution of whisker bridging, crack deflection and transformation. with increasing whisker content, AK, and AKd will be increased as ggested by eqns(5) and(6), which results in 4 RESULTS AND DISCUSSION rise in Kr. To drive the crack, Ko is needed to increase. leading to an enlargement of the trans- These parameters of SiCw/Zro2(2mol%Y203)/ formation zone. So AKs is increased. Whisker AlO3 ceramics are used to calculate the fracture toughening is beneficial to transformation. In con curves, Esicw=550 GPa, EA103=400 GPa, trast, for the same whisker content, with increasing EzO2=220GPa,E=5%,f=0.8,=700MPa The X-ray diffraction patterns show that about 20 vol% tetragonal ZrO2 has transformed into monoclinic ZrO2 in total ZrO2 particles during the fracture process of the composites. Thereb 30%SiCw Vi_m=0.2. The fracture toughness of AlO3 is 20%OSIC K4h0,=4.4 MPam/, and fracture toughness of 10%SiC Zro, which did not transform Kzo =3.4 MPam/2. For the whisker, o =8 GPa Iw=0.5um, and whisker length L=25 um. The friction coefficient of whisker/matrix (matrix con- sists of Al,O3 and Zro, which did not transform) interface is u=0.4. For the specimen, a0=2.5mm w=5mm, B=2.5mm, and the span L=20mm 00.030.060.090.12 Applying external stress intensity Kp, and then P can be given by eqn (13). Calculating Kr, if Fig. 4. R-curves vs whisker content in SiCw/ vol%Zro,/ K,<Kr, Kn increases. When K= Kn, the main crack a is allowed to extend a small increment la(=ao/2000). At each increment in Kp and da, the alculations of K and P are repeated until the main crack propagates in a unstable manner, and then a crack resistance curve. or R-curve vs the 10 crack growth length is obtained. At the point of 20%ZrO2 maximum load, Pmax, the fracture toughness, KIC and the corresponding contributions from trans- 10%Zro formation, whisker bridging and crack deflection △Kxc,△ Khe and△ Kde can be obtained. Figures 4 and 5 show the calculated R-curves for SiCw/ZrO2(2mol%Y2O3)/Al2O3 composites with different whisker content(Fig. 4)or ZrO, content (Fig. 5). When the crack propagates initially 00.030.060.090.12 transformation, whisker bridging and crack deflec tion all take place in the vicinity of the crack tip, so Fig. 5. R-curves vs ZrO2 content in 20 vol %/SiCw/ZrO2/ △Ks,△ Kh and△ Kd increase, which results in a Al2O3 ceramics
reinforcements. According to the proportion of Al2O3+(10, 20, 30 vol%) ZrO2+(10, 20, 30 vol%) SiCw, these powders and whiskers are mixed by ball milling for 24 h in an hydrous alcohol. the mixtures are dried and green-compacted at 250 MPa and then hot pressed at 1650C, 25MPa for 45 min. The temperature lies for hot pressing in the single tetragonal phase region of ZrO2-Y2O3 diagram. The fracture toughness is measured with an Instron-1186 testing machine using the singleedge notch 3-point bend specimen, 3042, with a notch depth, 2 mm. The volume percentage of tZrO2 in total ZrO2 is measured with X-ray diraction (XRD) on the as-polished and the fracture surfaces. 4 RESULTS AND DISCUSSION These parameters of SiCw/ZrO2(2mol%Y2O3)/ Al2O3 ceramics are used to calculate the fracture curves, ESiCw=550 GPa, EAl2O3=400 GPa, EZrO2= 220 GPa, "T=5%, f=0.8, c=700MPa. The X-ray diraction patterns show that about 20 vol% tetragonal ZrO2 has transformed into monoclinic ZrO2 in total ZrO2 particles during the fracture process of the composites. Thereby Vtÿm=0.2. The fracture toughness of Al2O3 is KAl2O3=4.4MPam1/2, and fracture toughness of ZrO2 which did not transform is KZrO2 =3.4 MPam1/2. For the whisker, w=8 GPa, rw=0.5m, and whisker length L=25m. The friction coecient of whisker/matrix (matrix consists of Al2O3 and ZrO2 which did not transform) interface is =0.4. For the specimen, a0=2.5 mm, W=5 mm, B=2.5 mm, and the span L=20 mm. Applying external stress intensity Kp, and then P can be given by eqn (13). Calculating Kr, if Kp < Kr; Kp increases. When Kr Kp, the main crack a is allowed to extend a small increment da(=a0/2000). At each increment in Kp and da, the calculations of Kr and P are repeated until the main crack propagates in a unstable manner, and then a crack resistance curve, or R-curve vs the crack growth length is obtained. At the point of maximum load, Pmax, the fracture toughness, KIC, and the corresponding contributions from transformation, whisker bridging and crack de¯ection, Ksc, Kbc and Kdc can be obtained. Figures 4 and 5 show the calculated R-curves for SiCw/ZrO2(2mol%Y2O3)/Al2O3 composites with dierent whisker content (Fig. 4) or ZrO2 content (Fig. 5). When the crack propagates initially, transformation, whisker bridging and crack de¯ection all take place in the vicinity of the crack tip, so Ks, Kb and Kd increase, which results in a rapid rise in fracture resistance, Kr. For further crack extension, a higher value of the applied Kp is required. With the further crack propagation, due to some whiskers which bridge the crack failing, a transformation wake zone is formed, the increase in Ks and Kb no longer rise remarkably, thereby the slope of R-curves gradually drops, and these curves will also tend to become parallel lines. The eective fracture toughnesses calculated are shown in Tables 1 and 2. For the same ZrO2 content, Ks, Kb and Kd increase with increasing whisker content, as shown in Table 1, it implies that an increment in whisker content will give rise to each contribution of whisker bridging, crack de¯ection and transformation. With increasing whisker content, Kb and Kd will be increased, as suggested by eqns (5) and (6), which results in a rise in Kr. To drive the crack, Kp is needed to increase, leading to an enlargement of the transformation zone. So Ks is increased. Whisker toughening is bene®cial to transformation. In contrast, for the same whisker content, with increasing Fig. 4. R-curves vs whisker content in SiCw/20 vol%ZrO2/ Al2O3 ceramics. Fig. 5. R-curves vs ZrO2 content in 20 vol%/SiCw/ZrO2/ Al2O3 ceramics. 524 G. M. Song et al.
Modelling of combined reinforcement of ceramic composites 525 Table 1. The toughness of SiCw/20 vol%zrO2/Al2o Transformation in ZrO2 is accompanied by exten- MPa m1/2 sive microcracking although the effects of micro- Measured cracking are thought of as small compared with △Kse△K△ Kde Kic K that of transformation. And microcracking is also beneficial to crack deflection. These more complex 1.14278537.31 146689689.10 toughening phenomena need further study 1.6159.65 9.87 REFERENCES Table 2. The toughness of 20 vol%SiCw/ZrO2/Al203, MPa m1/2 BECHER, P. F& WEL, G. C, Toughening behavior in SiC whisker-reinforced alumina.J. Am. Ceram. Soc. 6 Zro,(vol%) Calculated Measured 2. FABER.K. T ANS. A.G. Crack deflection Pro- △Ke△Kc△ Kde KIc Kic Metl.,31(1983)565-576 3. BENGISU, M. INAL, O. T.& TOSYALl. O, On 1.15108001558789 785 2.7080.6761.66 9.10 Mater,39(1991)2509-251 4.5004861.38310.22 1038 4. EVANS, A. G.& CANNON, R. M, Toughening of Metall.,34(5)(1986)761-800 5. EVANS.AG.& HeUer. A.h. review -Transforma ZrO2 content,△ Ks increases,but△ Kh and△Kdll tion toughening in ceramics: martensitic transformation decrease. The rise of transformation particle con in crack-tip stress fields. J. Am. Ceram. Soc., 63(5-6) (1980)241-248 tent gives rise to AKs. As a result of that, Kr is 6. ZHOU, Y, Microstructure and mechanical properties of increased, and the external applied load Kp has to ZrO -Y2O3 ceramics, Ph D. thesis, Harbin Institute of be increased for driving the crack which causes the Technology, Harbin, 1989(in Chinese). 7. LIN. G. Y, LEl. T C. ZHOU, Y.& WaNG, s.X. crack face opening displacement to increase Mechanical properties of Al2O3 and Al2O3+ ZrO2 cera- Therefore some whiskers bridging the crack face mics reinforced by SiC whiskers. J. Mater. Sci., 28(1993) will fail, and AKh decreased. Because the crack 2745-2749 8. LEL, T. C, GE, Q. L, ZHOU, Y.& WANG, s. x deflection is only related to the whisker bridging, as Microstructure and fracture behavior of an Al,O3-ZrO2- suggested by crack deflection model(eqn(6)), AKd ICw ceramic composite Ceram. Int, 20(1994)91-97. Then AKb decreases. Thereby the exist 9. MARSHALL. D.B. COX. B.N.& evaNs. A g. The of transformation particle is not beneficial to the mechanics of matrix cracking in brittle-matrix fiber posites. Acta Metall, 33(1985)2013-2021 toughening of whisker bridging or crack deflection. 10. VICTOR, C. Li, JIANG, W. Y&STANLEY,B,A micromechanical model of tension softening and brid ging toughening of short random fiber reinforced brittle natrix composites. J. Mech. Phys. Solids, 39(5)(1991) 5 SUMMARY I1. BUDIANSKY. B. HUTCHINSON lan A analytical model of combine toughening in cera BROPOLOUS,J C, Continuum theory of transforma- mics toughened with whiskers and transformation ramics. Int. J Struct. 19 (1983)337-355 particles is proposed based on three toughening 12. CHEN, I. C.& mOREL, P. E. E, Implications of mechanisms. whisker bridging. crack deflection and transformation. It is used to estimate quanti shear and dilatation effects. J. A. Ceram. Soc., 69(3) (1986)181-189 tatively their toughening contributions, and the 13. AMAZIGO, J C& BUDIANSKY, B.J., Interaction of calculated results of fracture toughness for SiC. articulate and transformation toughening. J. Mech ZrO2(2mol%Y203)/A12O3 ceramic composites 14. beCheR.PF. TIEGS. t.N. ogle. J. C.& War- show that the values of calculated toughness are in WICK, W.H., Toughening of ceramics by whisker rein good agreement with that of experimental results. forcement In Fracture mechanics of Ceramics, Vol. 7, ed There is interaction between the transformation R. C. Bradt. A. G. Evans, D. P. Hasselman F. F. Lange. Plenum Press. New York. 1986 639649 whisker bridging and crack deflection. Whisker 15. TAdA.H. PARIs.P c& IRWIN. G.r. The stress bridging and crack defection prompt transforma Analysis of Cracks Handbook. Del Research Corpora tion toughening. In contrast, transformation on, Hellertown, Pa, 1973. pp. 2. 16-27 6. baNSAL. P.P.& ard toughening produces a reduction to the toughen eighbor distances between uniformly distributed finite effects of whisker bridging and crack deflection les. Metallography, 5(1972)97-1l
ZrO2 content, Ks increases, but Kb and Kd all decrease. The rise of transformation particle content gives rise to Ks. As a result of that, Kr is increased, and the external applied load Kp has to be increased for driving the crack which causes the crack face opening displacement to increase. Therefore some whiskers bridging the crack face will fail, and Kb decreased. Because the crack de¯ection is only related to the whisker bridging, as suggested by crack de¯ection model (eqn (6)), Kd is decreased when Kb decreases. Thereby the exist of transformation particle is not bene®cial to the toughening of whisker bridging or crack de¯ection. 5 SUMMARY A analytical model of combine toughening in ceramics toughened with whiskers and transformation particles is proposed based on three toughening mechanisms, whisker bridging, crack de¯ection and transformation. It is used to estimate quantitatively their toughening contributions, and the calculated results of fracture toughness for SiCw/ ZrO2(2mol%Y2O3)/Al2O3 ceramic composites show that the values of calculated toughness are in good agreement with that of experimental results. There is interaction between the transformation, whisker bridging and crack de¯ection. Whisker bridging and crack defection prompt transformation toughening. In contrast, transformation toughening produces a reduction to the toughening eects of whisker bridging and crack de¯ection. Transformation in ZrO2 is accompanied by extensive microcracking although the eects of microcracking are thought of as small compared with that of transformation. And microcracking is also bene®cial to crack de¯ection. These more complex toughening phenomena need further study. REFERENCES 1. BECHER, P. F. & WEI, G. C., Toughening behavior in SiC whisker-reinforced alumina. J. Am. Ceram. Soc., 67 (1984) C267. 2. FABER, K. T. & EVANS, A. G., Crack de¯ection Process-I. Theory. Acta Metall., 31 (1983) 565±576. 3. BENGISU, M., INAL, O. T. & TOSYALI, O., On whisker toughening in ceramic materials. Acta Metall. Mater., 39 (1991) 2509±2517. 4. EVANS, A. G. & CANNON, R. M., Toughening of brittle solids by martensitic transformations. Acta Metall., 34(5) (1986) 761±800. 5. EVANS, A. G. & HEUER, A. H., Review-Transformation toughening in ceramics: martensitic transformation in crack-tip stress ®elds. J. Am. Ceram. Soc., 63(5±6) (1980) 241±248. 6. ZHOU, Y., Microstructure and mechanical properties of ZrO2-Y2O3 ceramics, Ph.D. thesis, Harbin Institute of Technology, Harbin, 1989 (in Chinese). 7. LIN, G. Y., LEI, T. C., ZHOU, Y. & WANG, S. X., Mechanical properties of Al2O3 and Al2O3+ZrO2 ceramics reinforced by SiC whiskers. J. Mater. Sci., 28 (1993) 2745±2749. 8. LEI, T. C., GE, Q. L., ZHOU, Y. & WANG, S. X., Microstructure and fracture behavior of an Al2O3-ZrO2- SiCw ceramic composite. Ceram. Int., 20 (1994) 91±97. 9. MARSHALL, D. B., COX, B. N. & EVANS, A. G., The mechanics of matrix cracking in brittle-matrix ®ber composites. Acta Metall., 33 (1985) 2013±2021. 10. VICTOR, C. Li., JIANG, W. Y. & STANLEY, B., A micromechanical model of tension softening and bridging toughening of short random ®ber reinforced brittle matrix composites. J. Mech. Phys. Solids, 39(5) (1991) 607±625. 11. BUDIANSKY, B., HUTCHINSON, J. W. & LANBROPOLOUS, J. C., Continuum theory of transformation toughening in ceramics. Int. J. Solids Struct., 19 (1983) 337±355. 12. CHEN, I. C. & MOREL, P. E. E., Implications of transformation plasticity in ZrO2-containing ceramics: I, shear and dilatation eects. J. Am. Ceram. Soc., 69(3) (1986) 181±189. 13. AMAZIGO, J. C. & BUDIANSKY, B. J., Interaction of particulate and transformation toughening. J. Mech. Phys. Solids, 36 (1980) 581±595. 14. BECHER, P. F., TIEGS, T. N., OGLE, J. C. & WARWICK, W. H., Toughening of ceramics by whisker reinforcement. In Fracture mechanics of Ceramics, Vol. 7, ed. R. C. Bradt, A. G. Evans, D. P. Hasselman & F. F. Lange. Plenum Press, New York, 1986, pp. 639±649. 15. TADA, H., PARIS, P. C. & IRWIN, G. R., The Stress Analysis of Cracks Handbook. Del Research Corporation, Hellertown, Pa., 1973, pp. 2, 16±27. 16. BANSAL, P. P. & ARDELL, A. J., Average nearestneighbor distances between uniformly distributed ®nite particles. Metallography, 5 (1972) 97±111. Table 1. The toughness of SiCw/20 vol%ZrO2/Al2O3, MPa m1/2 SiCw (vol%) Calculated Measured Ksc Kbc Kdc K0 IC KIC 10 2.219 0.316 1.142 7.853 7.31 20 2.708 0.676 1.466 8.968 9.10 30 3.092 0.901 1.615 9.65 9.87 Table 2. The toughness of 20 vol%SiCw/ZrO2/Al2O3, MPa m1/2 ZrO2 (vol%) Calculated Measured Ksc Kbc Kdc K0 IC KIC 10 1.151 0.800 1.558 7.898 7.85 20 2.708 0.676 1.66 8.968 9.10 30 4.50 0.486 1.383 10.22 10.38 Modelling of combined reinforcement of ceramic composites 525